Hyperborea, and the Hyperboreans, seem to have had an enduring life among the ancient Greeks and Romans, even if they couldn’t always agree on where it was. It first intrigued me because of the story that Apollo went there every winter.
The name comes from the Greek for “beyond the north wind”, since Boreas was the personification of the fourth, coldest wind. (See here for the other three Anemoi, and their story.) He was born in the mountainous north, and the story went that beyond those mountains was a paradise where men lived for hundreds of years, and when they died, they became swans.
These near-impassible mountains were known as the Riphean Mountains, and many Greek authors, spanning the time from Homer to Aristotle, mention them. They did not specify where these mountains were (“far away”, essentially) but later, the Romans took up the challenge and placed them definitely in the north. That was about all they agreed on. Pomponius Mela put them all the way into the Arctic Circle, while Pliny the Elder offered the Urals as candidates.
Over time various peoples were identified as the Hyperboreans, including the Scythians and the Celts. Both satisfied the basic conditions: not like us, far away, almost inaccessible.
Homer : a lost work (if it ever really existed) called the Epigoni, mentioned the Hyperboreans. Herodotus mentions it in book 4, chapter XXXII of the Histories. He then goes on in the next few chapters to tell the how the people of Delos (a major site for the cult of Apollo) received offerings from the Hyperboreans. (See below for more on Herodotus and the Hyperboreans.)
Pausanias: also connects Hyperborea to Delphi, in book 10 of his Description of Greece. He relates a tradition that the oracle itself was created by sons of the Hyperboreans, and also mentions that the second shrine built at Delphi was created by the Hyperboreans, from feathers and beeswax.
Posidonius: this ancient scholar’s works are mostly lost, but we have fragments in the form of quotes. One of them mentions the Hyperboreans. Frag. 103 (from the work of Apollonius of Rhodes) quotes him in contradiction to Herodotus, saying that while Herodotus does not believe the Hyperboreans exist, Posidonius does, and thinks they live around the Alps.
This has led to a lively debate over whether Posidonius thought that the Gauls who invaded northern Italy were the Hyperboreans. Considering that we don’t even know what Posidonius said, it seems unlikely to be settled any time soon.
Herodotus: is skeptical about the Hyperboreans. He mentions that Homer (above) and Hesiod speak of them, but that Scythians, who relate many other fantastic tales (about a one-eyed people, for example), do not have any tales that would match the Hyperboreans.
Diodorus Siculus: said that the Hyperboreans lived on an island beyond the land of the Celts. If he meant the continental Celts, then this could be either Britain or perhaps Scandinavia. He says that Apollo is honoured by them above all other gods.